For those looking for a more satisfying answer implied by the simple title here goes. The “αs” number quoted is a dimensionless unit so let’s pick a distance of 1 femtometer so that we can use newtons. The strong force between two gluons is about 150,000N at this distance, compared to 230N for electromagnetism. Electromagnetism weakens with the square of the distance and the strong force does a similar thing up to a point and then it becomes constant. At about 1.1 - 1.5 fm it “snaps”. The energy in the tension is enough to create another pair of gluons. To put it in perspective, the width of a proton is 0.85 fm. It’s all waves down there so my layman view is probably oversimplified.

> the strong force does a similar thing

No, in the heuristic approximation you are using here, the strong interaction does not weaken with distance; it strengthens with distance, so it takes more and more energy to try to pull two quarks apart, for example, as they get further apart (whereas the energy it takes to pull, say, an electron and a proton apart gets less and less as they get further apart).

So, for example, if you try to pull apart the quark and antiquark inside a pion, at a distance scale of roughly a femtometer, the energy required to pull the two quarks apart is large enough to create another quark-antiquark pair, and so you end up with two pions. You never get free quarks.

Similar remarks would apply to trying to pull a gluon out of, say, a glueball; you just end up making more gluons and making the glueball larger; you never get free gluons.

> At about 1.1 - 1.5 fm it “snaps”. The energy in the tension is enough to create another pair of gluons. To put it in perspective, the width of a proton is 0.85 fm. It’s all waves down there so my layman view is probably oversimplified.

That sort of makes intuitive sense, right? If the force were weaker so that it "snapped" at 10 femtometers, you'd expect protons themselves to be somewhere in that size range as well.

(Or am I totally wrong?)

Do you have the weak force number as well? I'm curious.

I _think_ I expect it to be quite high. My understanding is it's "weak" because it falls off quickly, past a certain distance, due to the force carrier having mass.

It’s pretty intuitive in the context of confinement theory. Intuitively we imagine something like a rubber band, as you add energy in the form of tension the material passes a threshold and as you say snaps. For confinement however as you add energy to the system it doesn’t snap, you simply reach the moment when you’ve added enough energy to the system to create a new particle pair that are also confined.

This is the explanation for why when we collide beams of protons at near c they don’t produce a new higher energy particle, but a massive shower of secondary and tertiary particles like pions and kaons as a result of the decay chain from initial pair production.